Weather Station: Space and Material Checks
0 / 14Weather Station: Space and Material Checks
Use geometry to plan equipment for recording temperature and rainfall.
Recording Panels
Find the area needed for each weather-station part. Use perpendicular heights. Ignore cutting waste.
1.
A parallelogram-shaped panel displays the week's temperature records. Its base is 24 cm, its perpendicular height is 15 cm, and its slanted side is 17 cm. Clear film covers one face.
How much film is needed? cm²
2.
A triangular marker identifies the rainfall-recording station. One face has an area of 84 cm² and a base of 14 cm. What is the perpendicular height?
3.
A six-sided backing for a temperature recorder starts as an 18 cm by 10 cm rectangle. A right triangle is cut from each of the two top corners. Each removed triangle has perpendicular legs of 4 cm and 3 cm. The removed triangles do not overlap.
What is the area of the remaining backing? cm²
4.
The shaded rectangles form a T-shaped panel for posting temperature and rainfall records. Each grid square represents 1 dm². The rectangles meet along an edge without overlapping. Weatherproof covering costs $3 per square decimeter.
What is the cost to cover one face of the entire panel? $
5.
A trapezoidal cover protects a rainfall log. Its area is 72 cm², and the perpendicular distance between its parallel sides is 8 cm. One parallel side is 7 cm long. How long is the other parallel side?
Collector Capacity
Use volume to check rain collectors and equipment parts. All stated collector dimensions are interior measurements.
6.
A rain collector has a flat rectangular bottom measuring 25 cm by 16 cm and vertical walls. After a storm, the water is 0.8 cm deep.
What volume of rainwater was collected? cm³
7.
A rain channel is a triangular prism. Its triangular cross section has a base of 10 cm and a perpendicular height of 6 cm. The channel is 22 cm long. A rainfall test fills it to the top.
How much water does the full channel hold? cm³
8.
Students compare two containers for storing collected rainwater. The cube has an inside edge length of 4 cm. The rectangular prism measures 8 cm by 4 cm by 3 cm inside. How much more water does the rectangular prism hold?
9.
A solid spacer supports a temperature sensor. It is a hexagonal prism, 5 cm long. Each hexagonal end consists of a 12 cm by 8 cm rectangle with a triangle attached to each 8 cm side. Each triangle has base 8 cm and perpendicular height 3 cm. These three regions meet only along edges.
What is the volume of the spacer? cm³
Weatherproof Surfaces
Identify exactly which faces need material before calculating. Ignore material thickness, seams, and overlap.
10.
A temperature sensor sits inside a square-prism shield. Each side of the square cross section is 9 cm, and the shield is 14 cm tall. Reflective material covers only the four vertical rectangular faces. Both square ends remain open.
What area receives reflective material? cm²
11.
A closed rectangular-prism housing protects the device that records temperature and rainfall. Its outside dimensions are listed below. Ventilation openings have a combined area of 16 cm². Paint covers all six outside faces except these openings.
| Length (cm) | Width (cm) | Height (cm) |
|---|---|---|
| 15 | 8 | 6 |
What total area is painted? cm²
12.
A triangular-prism hood keeps rain off the temperature recorder. Each triangular end has a horizontal base of 10 cm, a perpendicular height of 12 cm, and two sloping sides of 13 cm each. The hood is 18 cm long. Waterproof sheets cover only the two sloping rectangular faces, not the triangular ends or bottom. What area of sheet material is needed?
13.
A cube-shaped cover protects a rainfall recorder. Each outside edge is 7 cm long. All six faces need one coat of sealant, including the bottom. One tin covers 98 cm².
What is the minimum number of tins needed? tins
14.
A rectangular rain collector has an inside bottom measuring 10 cm by 8 cm and vertical walls 6 cm high. Today, the recorded water depth is 4 cm. A liner must cover the bottom and all four inside walls up to their full height, with no lid. Sam calculates the liner area as 10 × 8 + 2(10 × 4) + 2(8 × 4) = 224 cm². Explain the error and find the correct liner area.